Contact of Multi-Level Roughness with Flat Rigid or Perfectly Plastic Body

Abstract

The analysis carried out has shown that the most convenient way of creating the theory of deformation of multilevel roughness is to apply the composite materials methods. The application of a self-consistent method is preferable since it allows defining the effective (average) elastic parameters for all levels. The self-consistent method which has been applied in this investigation consists of the definition of composition of height distributions for all levels. Further, with the help of the composition distribution the elastic coefficients corresponding to the radii of peaks for each level separately have been determined. Finally, the coefficient have been averaged. The pressure applied has been defined as the sum of products of pressures for each level by weight coefficient. The values of the weight coefficient have been defined from self-consistent conditions. This approach allows obtaining the equation of deformation of multi-level roughness which has the same structure as the deformation of the one-level roughness in Demkin-Kragelski theory. The radii of peaks for each level and the reduced elastic modulus are supposed to have scattering. This is a generalisation of Demkin-Kragelski theory. The analytical equations for defining the relative displacement with the help of the average pressure have been obtained.